Also examine the Derivative Calculator
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The Integral Calculator lets you calculate integrals and antiderivatives of features online — for free!

Our calculator enables you to examine your solutions to calculus exercises. It helps you practice by reflecting you the complete working (step by action integration). All usual integration techniques and also even special attributes are supported.

You are watching: E^(x-2)

The Integral Calculator supports definite and also indefinite integrals (antiderivatives) as well as integrating features with numerous variables. You can likewise check your answers! interaction graphs/plots help visualize and much better understand the functions.

For an ext about how to usage the Integral Calculator, walk to "Help" or take a look in ~ the examples.

And now: Happy integrating!

Enter the function you want to incorporate into the Integral Calculator. Skip the "f(x) =" component and the differential "dx"! The Integral Calculator will display you a graphical version of her input while girlfriend type. Make certain that it shows exactly what girlfriend want. Use parentheses, if necessary, e.g. "a/(b+c)".

In "Examples", you have the right to see which attributes are supported by the Integral Calculator and how to use them.

When you"re excellent entering your function, click "Go!", and the Integral Calculator will display the result below.

In "Options", girlfriend can collection the variable of integration and also the integration bounds. If girlfriend don"t point out the bounds, just the antiderivative will be computed.

Clicking an instance enters it right into the Integral Calculator. Relocating the computer mouse over it reflects the text.

$x^2 - frac13y + 0.7z$$alpha x^2+eta x+gamma$$fracxx^2+1$$a(x^2+b)$$a_1x+K_ extabc$$x^-frac13$$mathrme^1-x$$sqrtx$$sqrt<7>x+1$$ln(x)$$log_8(x)$$|x|$$sin(x)$$cos(x)$$ an(x)$$arcsin(x)$$arccos(x)$$arctan(x)$$sec(x)$$sinh(x)$$operatornamearsinh(x)$$operatornameerf(x)$$operatornameB(x,y)$$operatornameGamma(x)$$operatornameSi(x)$$mathrme$$mathrmpi$$mathrmi$

Configure the Integral Calculator:

Variable of integration:Upper tied (to):Lower tied (from):Integrate numerically only?Simplify expressions?Simplify all roots?(√x² becomes x, no |x|)Use complex domain (ℂ)?Keep decimals?

The practice difficulty generator enables you to create as many random exercises as you want.

You uncover some configuration options and a proposed problem below. You deserve to accept it (then it"s input into the calculator) or create a new one.

Definite integralsIntegration by partsSubstitutionCompleting the squarePolynomials and powersExponential functionsTrigon./hyperb. FunctionsRational functionsInv. Trigon./hyperb. FunctionsLogarithmsSpecial functionsTricky integrals
Accept problemNext problem

Calculate the Integral that …Enter your very own Answer:

Exit "check answer" mode


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Not what you mean? Use parentheses! set integration variable and bounds in "Options".

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Above, get in the function to integrate. Variable the integration, integration bounds and an ext can be adjusted in "Options". Click "Go!" to start the integral/antiderivative calculation. The an outcome will be displayed further below.

How the Integral Calculator Works

For those with a technical background, the complying with section defines how the Integral Calculator works.

First, a parser analyzes the mathematical function. That transforms it into a type that is much better understandable through a computer, specific a tree (see figure below). In law this, the Integral Calculator needs to respect the order of operations. A specialty in mathematical expressions is the the multiplication sign deserve to be left out sometimes, for example we compose "5x" instead of "5*x". The Integral Calculator has to detect these cases and also insert the multiplication sign.

The parser is imposed in JavaScript, based on the Shunting-yard algorithm, and also can run directly in the browser. This permits for fast feedback while keying by transforming the tree into LaTeX code. MathJax takes care of displaying the in the browser.

When the "Go!" button is clicked, the Integral Calculator sends out the mathematical role and the settings (variable the integration and integration bounds) come the server, whereby it is analyzed again. This time, the function gets transformed into a type that deserve to be interpreted by the computer system algebra system Maxima.


Maxima takes care of actually computing the integral that the mathematics function. Maxima"s calculation is revolutionized to LaTeX again and is then presented to the user. The antiderivative is computed making use of the Risch algorithm, i m sorry is tough to know for humans. That"s why mirroring the measures of calculate is very an overwhelming for integrals.

In bespeak to present the steps, the calculator applies the very same integration methods that a human would apply. The regimen that go this has been emerged over several years and is composed in Maxima"s very own programming language. It consists of more than 17000 present of code. Once the integrand matches a well-known form, it applies fixed rules to settle the integral (e.g. Partial fraction decomposition because that rational functions, trigonometric substitution for integrands entailing the square root of a quadratic polynomial or integration by parts for commodities of certain functions). Otherwise, it tries different substitutions and transformations till either the integral is solved, time runs the end or over there is naught left come try. The calculator lacks the mathematical intuition the is an extremely useful because that finding one antiderivative, yet on the various other hand that can shot a big number the possibilities in ~ a quick amount that time. The action by step antiderivatives are frequently much much shorter and more elegant than those discovered by Maxima.

The "Checkanswer" attribute has to solve the difficult task of determining whether 2 mathematical expressions space equivalent. Their distinction is computed and also simplified as much as possible using Maxima. For example, this requires writing trigonometric/hyperbolic attributes in their exponential forms. If it deserve to be presented that the difference simplifies to zero, the job is solved. Otherwise, a probability algorithm is used that evaluates and compares both attributes at randomly liked places. In the situation of antiderivatives, the whole procedure is repeated with every function"s derivative, due to the fact that antiderivatives are enabled to different by a constant.

The interactive function graphs space computed in the browser and also displayed in ~ a canvas aspect (HTML5). For each role to be graphed, the calculator create a JavaScript function, which is then evaluated in little steps in stimulate to draw the graph. If graphing, singularities (e.g. Poles) are detected and also treated specially. The gesture regulate is imposed using Hammer.js.

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If you have any questions or concepts for improvements to the Integral Calculator, don"t hesitation to create me an e-mail.